In addition to the regular system of gaining experience and leveling up with it, Final Fantasy XII features a license system for gaining abilities and additional boosts. Each kill nets you an amount of LP (License Points) for each character, which are then consumed to buy licenses (tiles) on the license board. You cannot buy whichever tile whenever you want however, you must first buy a tile adjacent to the one you want to to make it available.
Each character has their own license board, although just how they look like depends on which version of the game you're playing.

License Board Types

Original License Board
The original license board was present only in the original release of the game on PS2. It features an identical board for all characters, except for special tiles which disappear from each character's board once unlocked on one board. These special licenses include the Quickenings and the Espers. For Quickenings, there are a total of 18 tiles on each board to begin with. This is enough to unlock all three Quickenings for each character with none left over. For Espers, the tiles appear on all boards once its corresponding Esper has been defeated in battle.

Zodiac Job License Boards
The Zodiac Job system is used in the Zodiac Job System (JP only) and The Zodiac Age versions of the game. There are 12 different jobs in this system, each corresponding to one of the basic zodiac, and which can be assigned to a character once you first gain control of them. In the Zodiac Job System you could only assign one job to each character, but in the Zodiac Age you can assign up to two. The jobs you assign do not need to be unique, you can assign the same job to as many characters as you want. To unlock the second job, you must first defeat Belias, and then obtain the Second License Board license tile on each character you wish to assign two jobs on.
Note that in case of shared licenses (the same ability being present on both the character's license boards), you cannot buy the license twice but instead every duplicate license is filled up on both boards the moment you buy it from one board. This is useful when you want to get to a far-away tile on one board, it might well be easier to get to the target tile's surrounding tiles on the other job's board, sometimes drastically reducing the LP required. Another specialty is the Quickening special tiles. They are shared between a character's boards as all tiles are, but there are four of them on each board, while you can only activate three at most. Once you've unlocked three Quickening tiles on a character the fourth Quickening tile on both that character's boards will disappear, preventing access to any license tiles that might be behind it.

License Boards

Here you will find brief descriptions of the license boards (jobs) available.

Original License Board

There are no restrictions on what each character can learn, and thus by the time you have every license learnt on every character, everyone can do and be anything.

Zodiac Job Boards

White Mage (Aries)
The healer of the party. Has basically no utility besides healing and buffing, and has low HP as well, although it can be slightly boosted via various Espers.
Can equip rods and mystic armor, so while their physical attack damage depends on STR, their armor boosts only MAG. If you want to do damage, best prepare a lot of ethers and your Holy spell.

Uhlan (Taurus)
A spear-user specialist with one of the highest physical attack prowess in the game. Has no magic capabilities to speak of, and their item using is mediocre. However, they do have access to Souleater and Sacrifice, both of which use the character's own HP for great effect. They also gain access to some Black Magicks via Quickening C and the Esper Chaos, but these will only be useful if the character's other job has magical affinity.
In addition to spears, Uhlans use heavy armor, allowing them to take hits.

Machinist (Gemini)
Swift item-users with a great variety of abilities to debuff, gain more items and attack in unconventional ways that are not dependent on the character's stats. They can also learn a small selection of mid-level Time Magicks via Famfrit should you wish to have that possibility.
Machinists equip guns, which ignore target's defense, and measures, which give various buffs to the target. Combine that with light armor being their armor of choice, and you have a straight-up support job.

Red Battlemage (Cancer)
The only job with access to Arcane Magicks, the Red Battlemage also has Green Magicks and mid-level White and Black Magicks in their arsenal. Both White and Black selection can be expanded upon with the use of some Espers. However, due to their big arsenal of magicks their stats can be lacking other than in terms of magic power, and you should carefully consider which job to supplement it with.
Red Battlemages can equip mystic armor, shields and maces, which depend on MAG to deal damage. Should you want for STR-based damage however, there is the possibility of unlocking greatswords via several Espers.

Knight (Leo)
Knights are sturdy defenders and attackers with a lot of HP and basically no capability for anything else. They can, however, unlock mid-level White Magick with the Espers Mateus and Hashmal, if you can spare them.
Their weapons of choice are swords and greatswords, and they can equip both heavy armor and shields.

Monk (Virgo)
Attackers capable of dishing out high damage even empty-handed, who also have a lot of HP. They have various debuffing abilities to help out the mages of the party, as well as several attacking abilities for themselves. It bears noting that they require the Esper Ultima to gain all tiers of Swiftness, and can access some White Magicks via Quickenings and Espers as well, although they don't have the magic power to wield them for much effect.
In addition to dishing it out empty-handed, monks can equip poles which ignore the target's magick defense when dealing damage. They also have access to light armor which raises their already high HP value through the roof.

Time Battlemage (Libra)
Surprisingly a very strong attacker, Time Battlemages nevertheless don't have access to weapons and abilities to make much use of it. They have access to all tiers of Time and Green Magicks, and are very quick at whatever they do.
Time Battlemages wear heavy armor, making them the most survivable mage with their high defenses. Their weapon choice consists of crossbows which deal damage based on STR, making the heavy armor a necessity. They also have the choice of wearing fairly high-level swords via the help of Espers.

Foebreaker (Scorpio)
Having access to all debuffing abilities, you might expect Foebreaker to be a support job but it has one of the highest physical offense capabilities in the game. To make up for it however, Foebreakers don't have much variety at all in what they can do, anything extra must be found from the character's second job.
Their weapons of choice are axes, hammers and handbombs. All of them deal highly varied damage that can either be insanely high or insanely low depending on how lucky you get. Their armor consists of heavy armor and shields.

Archer (Sagittarius)
Archer is basically a copy of Machinist with a different weapon and slightly better item-using capabilities. Their weapons are bows, which deal damage based on the user's SPD - appropriate as their armor type is light armor, which commonly raise speed. They do have access to high-level heavy armor though, via the Esper Shemhazai.

Black Mage (Capricorn)
Magickal attackers and not much else, Black Mages also have low HP. This can be somewhat mitigated via the Esper Famfrit, but their HP remains low even so. Their weapons arsenal is staves, which deal damage based on MAG, making their mystic armor doubly useful. They do have access to some heavy armor via the use of Espers if you want to make them more survivable instead though.

Bushi (Aquarius)
A magic-based physical attacker with relatively high HP, the Bushi can use physical attacking abilities and magical attacking abilities with the same ease - only problem is, they don't learn any spells natively, and so must rely on Shades of Black if you don't pair it with a mage job.
The Bushi wear katana, which like mentioned above deal damage based on the MAG stat. They also wear mystic armor to boost this, and can even equip Genji armor at the end of the game, although their defenses will be lacking until such a time. If you wish to go around this, you must use the Esper Zodiark to unlock more heavy armor.

Shikari (Pisces)
A basic attacker light on their feet, they have relatively good item using boosts but not much else. The Shikari wears light armor and shields, and equips daggers and ninja swords which both deal damage based on the user's SPD. Do note however, that there is no single save file in which your Shikari can wield all ninja swords equally. Each ninja sword tile is locked behind one of the four Quickening tiles, and you can only choose three of them to unlock.

Licenses

This section deals with what exactly is unlocked with each license available. An asterisk* next to a job's name on the 'board available' section means that either a Quickening or an Esper is required to unlock the tile in question.